After going through most of this thread it seems to me there some misconceptions about HDR and how it works. I've been shooting for HDR for about 4-5 years and this is what I've learned.
The HDR programs (in Photoshop or others, I use Photomatix-Pro) blend different exposures of the same image; the reason is that underexposed images will have greater detail in the high lights but almost pure black in the shadows. Alternately, an overexposed image will have blown out white highlights but good detail in the shadows. When shooting you need to have the exact same image for all, just different exposures, thus a tripod is mandatory. Aperture priority is also essential since you want the DOF to be the same in all images. The further you go either over or under exposure will render more details in the extreme ends of the final image (to a point). I use a Canon 60D ( a newer camera is just not in the budget, besides it's not the equipment but what you do with it (another UHH thread)), it has exposure bracketing. Basically you would use one normal exposure and the same number of over exposed images as under exposed images. With my Canon I can set the exposure bracketing for three exposures, I set this first set of three exposures so that the highest is at -2/3 step. Then set the next set of three exposures so that the darkest exposure is +2/3 step. I end up with six exposures, the two closest to a "normal" exposure tend to overlap in their dynamic range. The blended image keeps the details in the highlights as well as the shadows The range from high light detail to shadow detail (hence the name High Dynamic Range). Since you should shoot in Aperture Priority, it helps if nothing is moving making changes in shutter speed a non-issue. Moving objects will be recorded at different places, which will create a blur or out of focus areas. Finally, I shoot in raw only because I'm concerned with the detail in my images that I print at 11" x 17", which is the actual image size once it's processed and saved as a TIFF for the larger color gamut

There is no way to do exposure bracketing in aperture or shutter priority mode unless you also employ exposure compensation. As you already noted, if you change shutter speed, the aperture adjusts automatically - and you end up with two or more images with exactly the same exposure. The only change will be depth of field.

You need to be able to control each element. In this case it is likely to be easiest in manual mode, or use the camera's built-in HDR function if you have it.

UHH has an HDR section that can help you out:
https://www.uglyhedgehog.com/s-107-1.html

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Are you talking about the UHH emails you can get with links to the daily digest? I used to subscribe to those. At one time they stopped coming. I contacted UHH Admin and was told that one of the emails had gone to my spam folder. So they "blacklisted" me and stopped sending them. Eventually we worked it out. I suggest you contact Admin (send a Private Message). Hopefully they can fix it.

Edit: What CHG_CANON suggested works; it's what I do now (I got tired of getting the daily emails!)